On the ergodic theorem for affine actions on Hilbert space

TL;DR

This paper proves a new weak mean ergodic theorem for 1-cocycles linked to weakly mixing representations of amenable groups, advancing understanding of ergodic behavior in this mathematical context.

Contribution

It introduces a novel weak mean ergodic theorem specifically for 1-cocycles in the setting of weakly mixing representations of amenable groups.

Findings

Establishes a new weak mean ergodic theorem for 1-cocycles.

Connects ergodic properties with weakly mixing representations.

Provides insights into the behavior of affine actions on Hilbert spaces.

Abstract

This note establishes a new weak mean ergodic theorem for 1-cocycles associated to weakly mixing representations of amenable groups.